where \(G\)  is a finite group and \(|G|\)  is the number of elements in
\(G\) . With this inner product, for \( \chi _1, \chi _2,\dots , \chi _k\) 
which are characters of distinct (pairwisely non-equivalent)
irreducible representations, we have[1]}
\((\chi _i,\chi _j) = \delta _{ij}, \quad i, j = 1,2,\dots ,k.\) 
